A comparison of two approaches for improving direction-of-arrival estimates in the presence of non-white noise

Abstract

Many models of eigenstructure methods for direction-of-arrival problems are based on the assumption that the noise in signals is spatially white. This assumption may not be valid in practice. The presence of non-white noise in such models leads to degration in the estimates of the directions-of-arrival. The standard approach for improving the DOA estimates are either whitening or solving a generalized eigenvalue problem. In this paper, we examine the relationship between these two seemingly different approaches and show that whitening is in fact one of the many algorithms for solving the generalized eigenvalue problem.in terms of efficiency, numerical stability and accuracy. Experiments using whitening and QZ to estimate DOAs show that both QZ and whitening are equally robust when the computation is conducted in double-precision. This is true even under pathological cases when the noise is highly correlated. However, an analysis of the condition number of Σ, the noise covariance matrix, indicates that whitening may exhibit numerical instability in single-precision computation. A further set of experiments illustrates this fact. In practical situations, it is further established empirically that whitening is about two times faster than QZ.